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| 1 | On the 2~m-variable symmetric Boolean functions with maximum algebraic immunity显示文摘<正>The properties of the 2~m-variable symmetric Boolean functions with maximum al- gebraic immunity are studied in this paper.Their value vectors,algebraic normal forms,and algebraic degrees and weights are all obtained.At last,some necessary conditions for a symmetric Boolean function on even number variables to have maximum algebraic immunity are introduced. | QU LongJiang LI Chao | 2008 | Science in China(Series F)2008，51，2： | 12 |
| 2 | On the number of rotation symmetric Boolean functions显示文摘Rotation symmetric Boolean functions (RSBFs) have been used as components of different cryptosystems. This class of functions are invariant under circular translation of indices. In this paper, we investigated balanced RSBFs and 1st order correlation immune RSBFs. Based on constructive techniques, we give an accurate enumeration formula for n-variable balanced RSBFs when n is a power of a prime. Furthermore, an original and efficient method to enumerate all n-variable (n prime) 1st order correlationimmune functions is presented. The exact number of 1st order correlation immune RSBFs with 11 variables is 6925047156550478825225250374129764511077684773805520800 and the number of 13 variables has 189 digits. Then for more variables, we also provide a significant lower bound on the number of 1st order correlation immune RSBFs. | FU ShaoJing LI Chao QU LongJiang | 2010 | Science China(Information Sciences)2010，53，3： | 8 |
| 3 | SQUARE attack on block ciphers with low algebraic degree显示文摘By using an algebraic method, the mathematical foundation of SQUARE attack is studied in this paper. We point out that a SQUARE distinguisher exists if and only if the degree of the polynomial function between n-bit input which is active and n-bit output which is balanced is 2 n-2. And the algebraic method can also be used to determine the property of a balanced set after passed through a nonlinear S-box, by which in some cases we can find a SQUARE distinguisher with more rounds. The validity of SQUARE attack and the influence of the choice of S-box are also studied. If the round function of a Feistel cipher has a low algebraic degree, a SQUARE attack cannot recover the right keys in some special cases. However, SQUARE attack on SPN ciphers always holds. The relations among SQUARE attack and some other cryptanalytic method are studied, showing that if a cipher is breakable by SQUARE attack, then it is also breakable by the interpolation attack. | SUN Bing LI RuiLin QU LongJiang LI Chao | 2010 | Science China(Information Sciences)2010，53，10： | 4 |
| 4 | On the differential uniformities of functions over finite fields显示文摘In this paper, the possible value of the differential uniformity of a function over finite fields is discussed. It is proved that, the differential uniformity of a function over Fq can be any even integer between 2 and q when q is even; and it can be any integer between 1 and q except q-1 when q is odd. Moreover, for any possible differential uniformity t, an explicit construction of a differentially t-uniform function is given. | QU LongJiang LI Chao DAI QingPing KONG ZhiYin | 2013 | Science China Mathematics2013，56，7： | 4 |
| 5 | The Existence of a Class of Balanced Multi-output Rotation Symmetric Boolean Functions显示文摘A new characterization of balanced rotation symmetric(n, m)-functions is presented. Based on the characterization, the nonexistence of balanced rotation symmetric(p^r, m)-functions is determined, where p is an odd prime and m ≥ 2. And there exist balanced rotation symmetric(2~r, m)-functions for 2 ≤ m ≤ 2~r-r. With the help of these results, we also prove that there exist rotation symmetric resilient(2~r, m)-functions for 2 ≤ m ≤ 2~r-r-1. | DU Jiao FU Shaojing QU Longjiang LI Chao PANG Shanqi | 2018 | Chinese Journal of Electronics2018，27，5： | 2 |
| 6 | New constructions of q-variable 1-resilient rotation symmetric functions over F_p显示文摘Dear editor,Motivated by Refs.[1–10],we devote to constructing a class of q-variable 1-resilient rotation symmetric functions(RSFs)over the finite field F_p={0,1,...,p-1}in this letter.Throughout this letter,let p and q be different odd prime numbers. | Jiao DU Shaojing FU Longjiang QU Chao LI Shanqi PANG | 2016 | Science China(Information Sciences)2016，59，7： | 2 |
| 7 | Construction of even-variable rotation symmetric Boolean functions with maximum algebraic immunity显示文摘Rotation symmetric Boolean functions(RSBFs) have been used as components of different cryptosystems.In this paper,we investigate n-variable(n even and n≥12) RSBFs to achieve maximum algebraic immunity(AI),and provide a construction of RSBFs with maximum AI and nonlinearity.These functions have higher nonlinearity than the previously known nonlinearity of RSBFs with maximum AI.We also prove that our construction provides high algebraic degree in some case. | FU ShaoJing LI Chao MATSUURA Kanta QU LongJiang | 2013 | Science China(Information Sciences)2013，56，3： | 2 |
| 8 | New construction of perfect sequence set and low correlation zone sequence set显示文摘For a given binary ideal autocorrelation sequence,we construct a perfect sequence set by changing a few bits of the sequence.The set has a large size with respect to the period of its sequences.Based on the constructed perfect sequence set,a new class of low correlation zone sequence sets whose low correlation zone length can be chosen flexibly is obtained.Moreover,the new constructed low correlation zone sequence sets can attain Tang-Fan-Matsufuji’s bound with suitably chosen parameters. | XIONG Hai QU LongJiang LI Chao | 2013 | Science China(Information Sciences)2013，56，11： | 1 |
| 9 | On the covering structures of two classes of linear codes from perfect nonlinear functions显示文摘 | LI Chao LING San Qu Longjiang | 2009 | IEEE Transactions on Information Theory2009，55，1： | 1 |
| 10 | On the Construction of Boolean Functions with Optimal Algebraic Immunity 显示文摘 | Li Na QU Longjiang QI Wenfeng | 2008 | IEEE Transactions on Information Theory2008，54，3： | 1 |
| 11 | Constructing Symmetric Boolean Functions With Maximum Algebraic Immunity显示文摘 | QU Longjiang FENG Keqin LIU Feng | 2009 | IEEE Transactions on Information Theory2009，55，5： | 1 |
| 12 | On the Walsh spectrum of a family of quadratic APN functions with five terms显示文摘Recently,a family of quadratic APN functions was demonstrated by Bracken et al.to exist over F22k with k even and 3 k.This family of APN functions was firstly proposed by Budaghyan et al.and they exist provided the existence of a quadratic polynomial of the type x2s+1+cx2s+c2k x+1 with no zeros in F22k.Bracken et al.constructed such polynomials when k is even and 3 k.In this paper,we show that such polynomials exist for all even integers k.As a result,the APN functions over F22k exist for all even k.Furthermore,the Walsh spectra of these APN functions is shown to be the same as the one of the Gold APN functions.This gives a positive answer to one conjecture. | QU LongJiang TAN Yin LI Chao | 2014 | Science China(Information Sciences)2014，57，2： | 1 |
| 13 | Constructing-symmetric-Boolean-functions-with-maximum-algebraic-immunity显示文摘 | Qu Longjiang Feng Keqin Lin Feng | 2009 | IEEE Transactions on Information Theory2009，55，5： | 1 |
| 14 | A note on symmetric boolean functions with maximum algebraic immunity in odd number of variables显示文摘 | Qu Longjiang Li Chao Feng Keqin | 2007 | IEEE Trans2007，53，： | 1 |
| 15 | A lower dimension lattice attack on NTRU显示文摘Dear editor,Because of reasonably short length,easily created keys,high speed,low memory requirements and potential resistance to quantum attack,NTRU becomes one of the most popular public-key encryption systems and has drawn considerable attention.Motivated by[1–9],we devote to constructing a class of lower dimension lattices,called the IN-Lattice,and proposing a new lattice attack on NTRU cryptosystem. | Zhichao YANG Shaojing FU Longjiang QU Chao LI | 2018 | Science China(Information Sciences)2018，61，5： | 0 |
| 16 | Construction of Odd-Variable Boolean Function with Maximum Algebraic Immunity Using Univariate Polynomial Representation显示文摘To protect against algebraic attacks, a high algebraic immunity is now an important criterion for Boolean functions used in stream ciphers. In this paper, a new method based on a univariate polynomial representation of Boolean functions is proposed. The proposed method is used to construct Boolean functions with an odd number of variables and with maximum algebraic immunity. We also discuss the nonlinearity of the constructed functions. Moreover, a lower bound is determined for the number of Boolean functions with maximum algebraic immunity. | Zhao Wentao Fu Shaojing Li Chao Qu Longjiang | 2012 | China Communications2012，9，10： | 0 |
| 17 | Vulnerable Public Keys in NTRU Cryptosystem显示文摘In this paper the authors give an efficient bounded distance decoding(BDD for short)algorithm for NTRU lattices under some conditions about the modulus number q and the public key h.They then use this algorithm to give plain-text recovery attack to NTRUEncrypt and forgery attack on NTRUSign.In particular the authors figure out a weak domain of public keys such that the recent transcript secure version of NTRU signature scheme NTRUMLS with public keys in this domain can be forged. | Liqing XU Hao CHEN Chao LI Longjiang QU | 2020 | Chinese Annals of Mathematics,Series B2020，41，5： | 0 |
| 18 | A better bound for implicit factorization problem with shared middle bits显示文摘This paper presents our investigation of the implicit factorization problem, where unknown prime factors of two RSA moduli share a certain number of middle bits. The problem is described as follows. Let N_1 = p_1q_1, N_2 =p_2q_2 be two different n-bit RSA moduli, where q_1, q_2 are both αn-bit prime integers.Suppose that p_1, p_2 share tn bits at positions from t_1 n to t_2 n =(t_1 + t)n. Then this problem focuses on the condition about t, α to factor N_1, N_2 efficiently. At PKC 2010, Faug`ere et al. showed that N_1, N_2 can be factored when t > 4α. Subsequently, in 2015, Peng et al. improved this bound to t > 4α-3α~2. In this paper,we directly apply Coppersmith's method to the implicit factorization problem with shared middle bits, and a better bound t > 4α-4α^(3/2) is obtained. The correctness of our approach is verified by experiments. | Shixiong WANG Longjiang QU Chao LI Shaojing FU | 2018 | Science China(Information Sciences)2018，61，3： | 0 |
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